Showing papers on "Finite difference method published in 2008"
TL;DR: In this paper, a new full-vector finite difference discretization based on transverse magnetic field components was proposed for calculating the electromagnetic modes of optical waveguides with transverse, non-diagonal anisotropy.
Abstract: We describe a new full-vector finite difference discretization, based upon the transverse magnetic field components, for calculating the electromagnetic modes of optical waveguides with transverse, nondiagonal anisotropy. Unlike earlier finite difference approaches, our method allows for the material axes to be arbitrarily oriented, as long as one of the principal axes coincides with the direction of propagation. We demonstrate the capabilities of the method by computing the circularly-polarized modes of a magnetooptical waveguide and the modes of an off-axis poled anisotropic polymer waveguide.
371 citations
TL;DR: A numerical scheme to solve the two-dimensional damped/undamped sine-Gordon equation is proposed based on using collocation points and approximating the solution employing the thin plate splines radial basis function (RBF).
363 citations
TL;DR: An anomalous subdiffusion equation (ASub-DE) is considered and a new implicit numerical method (INM) and two solution techniques for improving the order of convergence of the INM for solving the ASub-DE are proposed.
Abstract: A physical-mathematical approach to anomalous diffusion is based on a generalized diffusion equation containing derivatives of fractional order. In this paper, an anomalous subdiffusion equation (ASub-DE) is considered. A new implicit numerical method (INM) and two solution techniques for improving the order of convergence of the INM for solving the ASub-DE are proposed. The stability and convergence of the INM are investigated by the energy method. Some numerical examples are given. The numerical results demonstrate the effectiveness of theoretical analysis. These methods and supporting theoretical results can also be applied to other fractional integro-differential equations and higher-dimensional problems.
357 citations
TL;DR: A simple method for the numerical solution of partial differential equations which embeds the problem within a Cartesian analog of the original equation, posed on the entire space containing the surface.
263 citations
TL;DR: This paper describes the simulation of a hypersonic vehicle configuration with detailed geometry and accurate boundary conditions using the compressible Euler equations, believed to be the most sophisticated calculation of this kind in terms of complexity of the geometry, the physical model, the numerical methods employed, and the accuracy of the solution.
241 citations
TL;DR: In this paper, the steady two-dimensional magneto-hydrodynamic flow of an incompressible viscous and electrically conducting fluid over a stretching vertical sheet in its own plane is analyzed.
Abstract: An analysis is made for the steady two-dimensional magneto-hydrodynamic flow of an incompressible viscous and electrically conducting fluid over a stretching vertical sheet in its own plane. The stretching velocity, the surface temperature and the transverse magnetic field are assumed to vary in a power-law with the distance from the origin. The transformed boundary layer equations are solved numerically for some values of the involved parameters, namely the magnetic parameter M, the velocity exponent parameter m, the temperature exponent parameter n and the buoyancy parameter λ, while the Prandtl number Pr is fixed, namely Pr = 1, using a finite difference scheme known as the Keller-box method. Similarity solutions are obtained in the presence of the buoyancy force if n = 2m−1. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. It is found that both the skin friction coefficient and the local Nusselt number decrease as the magnetic parameter M increases for fixed λ and m. For m = 0.2 (i.e. n = −0.6), although the sheet and the fluid are at different temperatures, there is no local heat transfer at the surface of the sheet except at the singular point of the origin (fixed point).
227 citations
TL;DR: Extensions of finite-difference time domain (FDTD) and finite-element time-domain (FETD) algorithms are reviewed for solving transient Maxwell equations in complex media in this article.
Abstract: Extensions of finite-difference time-domain (FDTD) and finite-element time-domain (FETD) algorithms are reviewed for solving transient Maxwell equations in complex media. Also provided are a few representative examples to illustrate the modeling capabilities of FDTD and FETD for complex media. The term complex media refers here to media with dispersive, (bi)anisotropic, inhomogeneous, and/or nonlinear properties present in the constitutive tensors.
210 citations
TL;DR: In this article, the SUPG method, a SOLD method and two types of FEM-FCT methods are compared with a 3D example with nonhomogeneous Dirichlet boundary conditions and homogeneous Neumann boundary conditions.
207 citations
TL;DR: In this article, a numerical scheme to solve the one-dimensional hyperbolic telegraph equation using collocation points and approximating the solution using thin plate splines radial basis function was proposed.
Abstract: Recently, it is found that telegraph equation is more suitable than ordinary diffusion equation in modelling reaction diffusion for such branches of sciences. In this article, we propose a numerical scheme to solve the one-dimensional hyperbolic telegraph equation using collocation points and approximating the solution using thin plate splines radial basis function. The scheme works in a similar fashion as finite difference methods. The results of numerical experiments are presented, and are compared with analytical solutions to confirm the good accuracy of the presented scheme. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008
197 citations
TL;DR: An immersed boundary method for the incompressible Navier-Stokes equations in irregular domains is developed using a local ghost cell approach that extends the solution smoothly across the boundary in the same direction as the discretization it will be used for.
193 citations
TL;DR: In this article, the authors used a three-dimensional implicit finite difference method with rectangular coordinate system to simulate the ground temperature and the borehole temperature profile for geothermal ground heat exchanger.
09 Jun 2008
TL;DR: In this article, a 3D time-domain finite-difference method was proposed to extract the frequency-domain wavefield by computing the terms of a discrete Fourier transform at each time step.
Abstract: Frequency-domain waveform inversion is typically perfomed using frequency-domain finite-difference modelling techniques. In 3D, these methods face significant computational challenges that limit any application to full-scale seismic applications. An alternative approach is to use a 3D time-domain finite-difference method and extract the frequency-domain wavefield by computing the terms of a discrete Fourier transform at each time step. This method combines the computational efficiency of 3D time-domain modelling while permitting casting the inverse problem in the frequency domain.
TL;DR: Five numerical methods for pricing American put options under Heston's stochastic volatility model are described and compared and it is suggested that the componentwise splitting method is the fastest one.
Abstract: Five numerical methods for pricing American put options under Heston's stochastic volatility model are described and compared. The option prices are obtained as the solution of a two-dimensional parabolic partial differential inequality. A finite difference discretization on nonuniform grids leading to linear complementarity problems with M-matrices is proposed. The projected SOR, a projected multigrid method, an operator splitting method, a penalty method, and a componentwise splitting method are considered. The last one is a direct method while all other methods are iterative. The resulting systems of linear equations in the operator splitting method and in the penalty method are solved using a multigrid method. The projected multigrid method and the componentwise splitting method lead to a sequence of linear complementarity problems with one-dimensional differential operators that are solved using the Brennan and Schwartz algorithm. The numerical experiments compare the accuracy and speed of the considered methods. The accuracies of all methods appear to be similar. Thus, the additional approximations made in the operator splitting method, in the penalty method, and in the componentwise splitting method do not increase the error essentially. The componentwise splitting method is the fastest one. All multigrid-based methods have similar rapid grid independent convergence rates. They are about two or three times slower that the componentwise splitting method. On the coarsest grid the speed of the projected SOR is comparable with the multigrid methods while on finer grids it is several times slower. ©John Wiley & Sons, Inc. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007
TL;DR: In this article, a numerical procedure, which is a combination of the finite element and finite difference methods, is also proposed to solve the chemical-dissolution front propagation problem in fluid-saturated porous media.
Abstract: The chemical-dissolution front propagation problem exists ubiquitously in many scientific and engineering fields. To solve this problem, it is necessary to deal with a coupled system between porosity, pore-fluid pressure and reactive chemical-species transport in fluid-saturated porous media. Because there was confusion between the average linear velocity and the Darcy velocity in the previous study, the governing equations and related solutions of the problem are re-derived to correct this confusion in this paper. Owing to the morphological instability of a chemical-dissolution front, a numerical procedure, which is a combination of the finite element and finite difference methods, is also proposed to solve this problem. In order to verify the proposed numerical procedure, a set of analytical solutions has been derived for a benchmark problem under a special condition where the ratio of the equilibrium concentration to the solid molar density of the concerned chemical species is very small. Not only can the derived analytical solutions be used to verify any numerical method before it is used to solve this kind of chemical-dissolution front propagation problem but they can also be used to understand the fundamental mechanisms behind the morphological instability of a chemical-dissolution front during its propagation within fluid-saturated porous media. The related numerical examples have demonstrated the usefulness and applicability of the proposed numerical procedure for dealing with the chemical-dissolution front instability problem within a fluid-saturated porous medium. Copyright © 2007 John Wiley & Sons, Ltd.
TL;DR: In this article, the energy conservation properties of a hydrostatic, Boussinesq, coastal ocean model using a classic finite difference method are investigated. But the authors do not consider the effect of the motion of the free surface on energy conservation.
TL;DR: An implicit and an explicit difference methods for the FR-subDE, a fractional reaction–subdiffusion equation in which both the motion and the reaction terms are affected by the subdiffusive character of the process.
TL;DR: In this paper, a new approach for the estimation of apparent thermal diffusivity of foods at different drying temperatures was explored, analysed and discussed in this work, where temperature versus time was obtained numerically at the center of the food (banana, “nanicao” variety) using the 1D Fourier equation with drying temperatures in the range between approximately 17-65°C and moisture content in range between 0.01 and 3.43 (dry basis).
TL;DR: In this article, a three-dimensional unconditionally stable locally-one-dimensional finite-difference time-domain (LOD-FDTD) method is proposed and is proved unconditional stable analytically.
Abstract: A three-dimensional unconditionally-stable locally-one-dimensional finite-difference time-domain (LOD-FDTD) method is proposed and is proved unconditionally stable analytically. In it, the number of equations to be computed is the same as that with the conventional three-dimensional alternating direction implicit FDTD (ADI-FDTD) but with reduced arithmetic operations. The reduction in arithmetic operations leads to approximately 20% less computational time in comparisons with the ADI-FDTD method.
TL;DR: In this article, a code for solving the coupled Einstein-hydrodynamics equations to evolve relativistic, self-gravitating fluids is presented, which accurately evolves equilibrium stars and accretion flows.
Abstract: We present a code for solving the coupled Einstein-hydrodynamics equations to evolve relativistic, self-gravitating fluids. The Einstein field equations are solved in generalized harmonic coordinates on one grid using pseudospectral methods, while the fluids are evolved on another grid using shock-capturing finite difference or finite volume techniques. We show that the code accurately evolves equilibrium stars and accretion flows. Then we simulate an equal-mass nonspinning black hole-neutron star binary, evolving through the final four orbits of inspiral, through the merger, to the final stationary black hole. The gravitational waveform can be reliably extracted from the simulation.
TL;DR: In this paper, an extended finite element method (XFEM) and the level set method are combined with a comprehensive level set update scheme with velocity extensions to simulate finger formation and finger-tip splitting in biofilms.
Abstract: This paper presents a computational technique based on the extended finite element method (XFEM) and the level set method for the growth of biofilms. The discontinuous-derivative enrichment of the standard finite element approximation eliminates the need for the finite element mesh to coincide with the biofilm–fluid interface and also permits the introduction of the discontinuity in the normal derivative of the substrate concentration field at the biofilm–fluid interface. The XFEM is coupled with a comprehensive level set update scheme with velocity extensions, which makes updating the biofilm interface fast and accurate without need for remeshing. The kinetics of biofilms are briefly given and the non-linear strong and weak forms are presented. The non-linear system of equations is solved using a Newton–Raphson scheme. Example problems including 1D and 2D biofilm growth are presented to illustrate the accuracy and utility of the method. The 1D results we obtain are in excellent agreement with previous 1D results obtained using finite difference methods. Our 2D results that simulate finger formation and finger-tip splitting in biofilms illustrate the robustness of the present computational technique. Copyright © 2007 John Wiley & Sons, Ltd.
TL;DR: In this article, a model order reduction method is developed and applied to 1D diffusion systems with negative real eigenvalues, and residues with similar eigen values are grouped together to reduce the model order.
Abstract: A model order reduction method is developed and applied to 1D diffusion systems with negative real eigenvalues. Spatially distributed residues are found either analytically (from a transcendental transfer function) or numerically (from a finite element or finite difference state space model), and residues with similar eigenvalues are grouped together to reduce the model order. Two examples are presented from a model of a lithium ion electrochemical cell. Reduced order grouped models are compared to full order models and models of the same order in which optimal eigenvalues and residues are found numerically. The grouped models give near-optimal performance with roughly 1/20 the computation time of the full order models and require 1000―5000 times less CPU time for numerical identification compared to the optimization procedure.
TL;DR: In this paper, an improved immersed boundary method for simulating incompressible viscous flow around an arbitrarily moving body on a fixed computational grid was presented, which combined the feedback foreing scheme of the virtual boundary method with Peskin's regularized delta function approach.
Abstract: We present an improved immersed boundary method for simulating incompressible viscous flow around an arbitrarily moving body on a fixed computational grid. To achieve a large CFL number and to transfer quantities between Eulerian and Lagrangian domains effectively, we combined the feedback foreing scheme of the virtual boundary method with Peskin’s regularized delta function approach. Stability analysis of the proposed method was carried out for various types of regularized delta function. The stability regime of the 4-point regularized delta function was much wider than that of the 2-point delta function. An optimum regime of the feedback forcing is suggested on the basis of the analysis of stability limits and feedback forcing gains. The proposed method was implemented in a finite difference and fractional step context. The proposed method was tested on several flow problems and the findings were in excellent agreement with previous numerical and experimental results.
TL;DR: The newly proposed method is based on the Hopf–Cole transformation, which transforms the original nonlinear Burgers’ equation into a linear heat equation, and transforms the Dirichlet boundary condition into the Robin boundary condition, which leads to an implicit fourth-order compact finite difference scheme.
TL;DR: In this article, the most promising of these SOLD methods are investigated in more detail for P 1 and Q 1 finite elements, the dependence of the results on the mesh, the data of the problems and parameters of the methods are studied analytically and numerically.
TL;DR: In this paper, the non-uniform heat source/sink effect on the flow and heat transfer from an unsteady stretching sheet through a quiescent fluid medium extending to infinity is studied.
TL;DR: This paper presents a fast and accurate simulation method for the permeability of a textile reinforcement, based on a finite difference discretisation of the Stokes equations, for single layer, multi-layer and sheared models.
TL;DR: Numerical results obtained for the positive taper angle show that the blood flow characteristics such as the axial velocity profiles, flow rate and wall shear stress have lower values, while the resistive impedances have higher values than the Newtonian model.
TL;DR: In this article, a fully coupled isothermal elastohydrodynamic problem using a finite element discretization of the corresponding equations was solved by using variable unstructured meshing and different types of elements within the same model.
Abstract: The solution of the elastohydrodynamic lubrication (EHL) problem involves the simultaneous resolution of the hydrodynamic (Reynolds equation) and elastic problems (elastic deformation of the contacting surfaces) Up to now, most of the numerical works dealing with the modeling of the isothermal EHL problem were based on a weak coupling resolution of the Reynolds and elasticity equations (semi-system approach) The latter were solved separately using iterative schemes and a finite difference discretization Very few authors attempted to solve the problem in a fully coupled way, thus solving both equations simultaneously (full-system approach) These attempts suffered from a major drawback which is the almost full Jacobian matrix of the nonlinear system of equations This work presents a new approach for solving the fully coupled isothermal elastohydrodynamic problem using a finite element discretization of the corresponding equations The use of the finite element method allows the use of variable unstructured meshing and different types of elements within the same model which leads to a reduced size of the problem The nonlinear system of equations is solved using a Newton procedure which provides faster convergence rates Suitable stabilization techniques are used to extend the solution to the case of highly loaded contacts The complexity is the same as for classical algorithms, but an improved convergence rate, a reduced size of the problem and a sparse Jacobian matrix are obtained Thus, the computational effort, time and memory usage are considerably reduced
TL;DR: In this article, a Riesz fractional advection-dispersion equation with an initial condition (RFADE-IC) is derived from the kinetics of chaotic dynamics.
Abstract: In this paper, we consider a Riesz fractional advection-dispersion equation (RFADE), which is derived from the kinetics of chaotic dynamics. The RFADE is obtained from the standard advection-dispersion equation by replacing the first-order and second-order space derivatives by the Riesz fractional derivatives of order a e (0, 1) and fi e (1, 2], respectively. We derive the fundamental solution for the Riesz fractional advection-dispersion equation with an initial condition (RFADE-IC). We investigate a discrete random walk model based on an explicit finite-difference approximation for the RFADE-IC and prove that the random walk model belongs to the domain of attraction of the corresponding stable distribution. We also present explicit and implicit difference approximations for the Riesz fractional advection-dispersion equation with initial and boundary conditions (RFADE-IBC) in a finite domain. Stability and convergence of these numerical methods for the RFADE-IBC are discussed. Some numerical examples are given to show that the numerical results are in good agreement with our theoretical analysis.
TL;DR: In this article, a model of a curved cable-beam, geometrically nonlinear and able to torque, was used to account for quasi-steady aerodynamic forces, including the effect of static swing of the cable and dynamic twist of the cross-section.